Part of the deal, of course, it would be that the ads in question will not be intrusive, disturbing or spying on you, they would not be massive and CPU/memory hungry (if in e.g. Flash), however, they would be allowed to download new ads every few days and possibly store them locally. A few other details of course will need to be cleared out. Some may say that "ads do not work". Well, these OSS projects have nothing to lose. If the idea won't work, well, it won't work. Life will go on as it did before.
However, would an ad-sponsored environment be against the Free Software or OSI or BSD philosophy, or it would merely be a way to help your favorite project and help it financially to pay for testing hardware, web servers, CVS servers, even "marketing" etc. Naturally, if you are a bit capable with C/C++, you could freely recompile the OSS project and remove the ad splash screen - but how ethical that would be?
Ideas like these, at first might not sound very sexy, but let's face it: if Lindows was doing something like this instead of that US$99 Click-n-Run thing, they would have today more credibility among the Linux community. Opera seems to do well with ad-sponsoring too, and in fact, their ads are not intrusive at all (especially if you shuffle the toolbars around the ad, so you utilize the available space better).
Update: The poll is now closed. Thank you all for voting. Results are following.